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Solve using elimination.\newline−9x−6y=3-9x - 6y = 3\newline9x+7y=−89x + 7y = -8\newline(_____, _____)

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Q. Solve using elimination.\newline−9x−6y=3-9x - 6y = 3\newline9x+7y=−89x + 7y = -8\newline(_____, _____)
  1. Write Equations: Write down the system of equations.\newline−9x−6y=3-9x - 6y = 3\newline9x+7y=−89x + 7y = -8
  2. Add Equations: Add the two equations together to eliminate the xx variable.\newline(−9x−6y)+(9x+7y)=3+(−8)(-9x - 6y) + (9x + 7y) = 3 + (-8)
  3. Eliminate x: Perform the addition to eliminate the x variable.\newline−9x+9x−6y+7y=3−8-9x + 9x - 6y + 7y = 3 - 8\newline0x+y=−50x + y = -5\newlineThis simplifies to y=−5y = -5.
  4. Substitute yy: Substitute y=−5y = -5 into one of the original equations to solve for xx. We'll use the second equation: 9x+7y=−89x + 7y = -8.\newline9x+7(−5)=−89x + 7(-5) = -8
  5. Solve for x: Perform the multiplication and solve for x.\newline9x−35=−89x - 35 = -8
  6. Isolate x: Add 3535 to both sides of the equation to isolate the xx term.\newline9x−35+35=−8+359x - 35 + 35 = -8 + 35\newline9x=279x = 27
  7. Final Solution: Divide both sides by 99 to solve for xx.9x9=279\frac{9x}{9} = \frac{27}{9}x=3x = 3

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